Topic 10 Classwork Assignment Problem 1: The set {2, 4, 6} is a population data set. (a) Fill in the table and make a bar graph of “Frequency vs Data Value” for the population data set. Is the population bar graph symmetric or non- symmetric? Find the mean, μ, and the standard deviation, σ, of the population. Data Value, x Frequency, f (b) Find all samples of size n = 2 for the population data set and then calculate the sample mean of each sample. Find the mean of the sample means, μx̅ and the standard deviation of the sample means, σx̅ . Sample Sample Mean, 𝐱̅ (c) Fill in the table and make a bar graph of “Frequency vs Sample Mean” for the sample of size n = 2. Is σ the bar graph of sample means symmetric or non- symmetric? Is μx̅ = μ? Is σx̅ = n? √ Sample Mean, 𝐱̅ Frequency, f Problem 2: The mean of a symmetric population data set is μ = 14.3 with a standard deviation σ = 2.8. Samples are drawn from the population data set and a sampling distribution of sample means is constructed for each sample. Find the mean of the sample means, μx̅ , and the standard deviation of the sample means, σx̅ , as is predicted by the Central Limit Theorem, for samples of each of the following sizes. σ Hint: μx̅ = μ and σx̅ = n √ (a) n = 10 (b) n = 30 (c) n = 100 Problem 3: The mean of a non-symmetric population data set is μ = 5.3 with a standard deviation σ = 1.2. Samples are drawn from the population data set and a sampling distribution of sample means is constructed for each sample. Find the mean of the sample means, μx̅ , and the standard deviation of the sample means, σx̅ , as is predicted by the Central Limit Theorem, for samples of each of the following sizes. σ Hint: μx̅ = μ and σx̅ = n √ (a) n = 10 (b) n = 30 (c) n = 100 Problem 4: Samples are drawn from the following population data set and a histogram of sample means is constructed for each sample. (a) According to the Central Limit Theorem, should the histogram of sample means of samples of size 10 drawn from this population be symmetric or non-symmetric? (b) According to the Central Limit Theorem, should the histogram of sample means of samples of size 30 drawn from this population be symmetric or non-symmetric? (c) According to the Central Limit Theorem, should the histogram of sample means of samples of size 100 drawn from this population be symmetric or non-symmetric? Problem 5: Samples are drawn from the following population data set and a histogram of sample means is constructed for each sample. (a) According to the Central Limit Theorem, should the histogram of sample means of samples of size 10 drawn from this population be symmetric or non-symmetric? (b) According to the Central Limit Theorem, should the histogram of sample means of samples of size 30 drawn from this population be symmetric or non-symmetric? (c) According to the Central Limit Theorem, should the histogram of sample means of samples of size 100 drawn from this population be symmetric or non-symmetric?
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